We once had Yemenite guests for pesach. They baked their own matza in a sort of barrel as an oven. As children, my parents let us eat it. So it was soft like pitta, although more burnt that a regular pitta. The pasuk calls matza, “uggos matzos”, which translates simply as, matza cake.
If you have a yemenite community where you are, maybe get an invite there for pesach. (Disclaimer – You may want to get guidance from a Rav first)